.-
help for ^somersd^              (STB-55: snp15; STB-57: snp15.1; STB-58: snp15.2)
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Somers' D or Kendall's tau-a with confidence intervals
-------------------------------------------------------

	^somersd^     varlist [weight] [^if^ exp] [^in^ range]
			[,^cl^uster^(^varname^)^ ^l^evel^(^#^)^ ^ta^ua  ^td^ist
			^tr^ansf^(^transformation_name^)^ ^ci^matrix^(^new_matrix^)^ ]

where transformation_name is one of

	^iden^ | ^z^ | ^asin^ | ^rho^ | ^zrho^

^fweight^s, ^iweight^s and ^pweight^s are allowed; see help ^weight^s.


Description
-----------

^somersd^ calculates values of Somers' D or Kendall's tau-a for the first
variable of varlist as a predictor of each of the other variables in varlist,
with estimates and jackknife variances and confidence intervals output as if
for the parameters of a maximum likelihood fit. It is possible to use @lincom@
to output confidence limits for differences between the population Somers' D or
tau-a values.


Options for use with ^somersd^
----------------------------

^cluster(^varname^)^ specifies the variable which defines sampling clusters.
    If ^cluster^ is defined, then the between-cluster Somers' D or tau-a is
    calculated, and the variances are calculated assuming that the data are
    sampled independently from a population of clusters, rather than from a
    population of observations.

^level(^#^)^ specifies the confidence level, in percent, for confidence intervals
    of the estimates; see help for @level@.

^taua^ causes ^somersd^ to calculate Kendall's tau-a. If ^taua^ is absent, then
    Somers' D is calculated.

^tdist^ specifies that the estimates are assumed to have a
    t-distribution with n-1 degrees of freedom, where n is the number of
    clusters or the number of observations if ^cluster^ is not specified.

^transf(^transformation_name^)^ specifies that the estimates are to be transformed,
    defining a confidence level for the transformed population value. ^iden^
    (identity or untransformed) is the default. ^z^ specifies Fisher's z (the
    hyperbolic arctangent), ^asin^ specifies Daniels' arcsine, ^rho^ specifies
    Greiner's rho (Pearson correlation estimated using Greiner's relation), and
    ^zrho^ specifies the z-transform of Greiner's rho.

^cimatrix(^new_matrix^)^ specifies an output matrix to be created, containing
    estimates and confidence limits for the untransformed Somers' D, Kendall's
    tau-a or Greiner's rho parameters. If ^transf()^ is specified, then the
    confidence limits will be asymmetric and based on symmetric confidence
    limits for the transformed parameters. This option (like ^level^) may be
    used in replay mode as well as in non-replay mode.


Remarks
-------

Somers' D is defined as

^D(Y|X)=tau-a(X,Y)/tau-a(X,X)^

In the case of a binary x-variable, Somers' D is the parameter tested
for a zero value by the Mann-Whitney U-test. In the case of paired data,
the Wilcoxon paired ranksum test tests a zero value for D(Y|X), where X is the
sign of a paired difference and Y is the absolute value of the same paired
difference. The covariance matrix is estimated by jackknifing the underlying
U-statistics. Taylor polynomials are used to calculate variances for Somers' D,
Kendall's tau-a and their transformations.


Examples
--------

 . ^somersd foreign mpg weight^

 . ^somersd foreign mpg weight,tr(z)^

 . ^somersd mpg weight displ,taua tr(z) cluster(manuf)^


Author
------

Roger Newson, Guy's, King's and St Thomas' School of Medicine, London, UK.
email: ^roger.newson@@kcl.ac.uk^


Also see
--------

 Manual:  ^[R] spearman, [R] signrank^
    STB:  STB-55: snp15; STB-57: snp15.1; STB-58: snp15.2
On-line:  help for @ktau@, @ranksum@, help for @jknife@ if installed